Early action and early decision applications are usually due at the end of October. This means taking your SAT no later than the October of your Upper 6/ Grade 12 year and your SAT Subject Tests no later than November. Regular decision applications are usually due at the end of December which means taking your SAT no later than December and your SAT Subject Tests no later than January.
Many schools, especially in Florida and California, have later deadlines (January and February) and some have rolling admissions deadlines right up until May. However, pay attention to financial aid deadlines, which may be much earlier.
You can apply to most schools by applying through Common App. To begin, create an account on www.commonapp.org, select schools and start filling out the application. For schools that are not on the Common App, there are three main alternatives: Coalition App, Universal App and school-specific applications. Their websites should have more information.
There is obviously a lot more that goes into admissions than this overview, but hopefully this is enough to get you started.